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Question
If the following pair of the triangle is congruent? state the condition of congruency:
In ΔABC and ΔPQR, BC = QR, ∠A = 90°, ∠C = ∠R = 40° and ∠Q = 50°.
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Solution
In ΔPQR
∠R = 40°, ∠Q = 50°
∠P + ∠Q + ∠R = 180° ...[Sum of all the angels in aa triangle = 180°]
⇒ ∠P + 50° + 40° = 180°
⇒ ∠P + 90° = 180°
⇒ ∠P = 180° - 90°
⇒ ∠P = 90°
In ΔABC and ΔPQR
∠A = ∠P
∠C = ∠R
BC = QR
By Angle-Angle-Side criterion of congruency, the triangles
ΔABC and ΔPQR are congruent to each other.
∴ ΔABC ≅ ΔPQR
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